Low c-differential uniformity for functions modified on subfields

In this paper, we construct some piecewise defined functions, and study their c-differential uniformity. As a by-product, we improve upon several prior results. Further, we look at concatenations of functions with low differential uniformity and show several results. For example, we prove that given beta(i) (a basis of F-qn over F-q), some functions f(i) of c-differential uniformities delta(i), and L-i (specific linearized polynomials defined in terms of beta(i)), 1 <= i <= n, then F(x) = Sigma(n)(i=1) beta(i)f(i) (L i(x)) has c-differential uniformity equal to Pi(n)(i=1) delta(i).